| Prerequisites |
Math 116,
156 or 186 |
| Credits |
4 credits |
| Alternatives |
Math 285
(Honors Calculus III) is a somewhat more
theoretical course which covers the same material. |
Subsequent
Courses |
For students intending to major in mathematics
or who have some interest in the theory of mathematics as well as its applications,
the appropriate sequel is Math 217
(Linear Algebra). Students who intend to
take only one further mathematics course and need differential equations
should take Math 216
(Introduction to Differential Equations) |
| Textbook |
You can use either one of the following two books (if you have the 6th edition of this book, see here):
- Calculus
(an excellent textbook, can be a good reference for
single-variable calculus)
- Multivariable
Calculus
(Later chapters of the Calculus
book, lighter and easier to carry around)
by James Stewart, Seventh edition,
Brooks/Cole;
2008
|
Course
Description |
The sequence Math 115-116-215 is the standard
complete introduction to the concepts and methods of calculus. It is taken
by the majority of students intending to major in mathematics, science,
or engineering as well as students heading for many other fields. The emphasis
is on concepts and solving problems rather than theory and proof. |
Course
Outline |
- Vectors
- Parametric Curves
- Functions of Two and Three Variables.
- Partial Derivatives.
|
- Multiple Integrals.
- Calculus of Vector Fields.
- Curl and Divergence.
- Green's, Stokes', and Divergence Theorems
|
|
Course
Components |
- Web Homework: 10%
- Written Homework: 10%
- First Exam (12.1-14.7): 25%
- Second Exam (14.8-16.3): 25%
- Final Exam (cumulative,
emphasis on Chapter 16): 30%
|
Exam
Policies |
- Calculators and Notes are not allowed on the midterms
and final.
- You can reschedule an exam only due to a serious conflict, illness,
or family emergency. If possible, you should discuss any such conflict
with your instructor well in advance of the exam date.
- If you need any special arrangements for the exams, you
should let your instructor know about it during the first two
weeks of the semester.
|
| Gateway |
There is a gateway test for this course, covering integrals
for single variable calculus. If you master the skills needed to pass the gateway test, you have a much better chance to do well in the course. |
Maple
Laboratory |
The geometry underlying multivariable calculus is
three-dimensional. Therefore, we meet once a week in a computer
lab to use the Computer Algebra System
Maple
to create graphs of curves and surfaces in space that are
otherwise very difficult to visualize, and to evaluate some of the
mathematical expressions we obtain. You will use
Maple in most of the lab periods, and on some of the
written homework problems. You will not be evaluated on your
understanding of Maple on exams.
Maple is installed on any of the SITEs labs on campus. You can also use VirtualSites
(http://virtualsites.umich.edu) to get a remote desktop on a campus server
that will have Maple.
|
Web
Homework |
There are
several
on-line problem sets (including "Set 0", an introductory set
explaining how to use the system, which is also graded). You
should start on web homeworks early. Homeworks start at 8 am on
the day that they open and close at 11:59 pm on the day they
are due. You are allowed six attempts for each problem. You can
get partial credit on a multiple parts problem. Each set
consists of 5-10 problems. More
answers to commonly asked questions can be found in
Web
Homework FAQ. About a day after the due date the correct
answers to the set are available. You must complete all of
each web homework set for full credit on the web homework.
|
Written
Homework |
In addition to web homework, there are
written homework sets
due approximately weekly. These assignments are due to your
GSI in lab. Due dates can be found on the course syllabus.
Administrative overhead prevents us from grading all problems on
each set, but you should complete them all. On each set, three
problems will be selected at random and graded (out of 5 points
each). You will get another 5 points if you complete all other problems.
Thus each homework set will be worth 20 points. The written homework on which you get the lowest
score will be dropped when calculating your course average.
|
